2 citations · 6 across the 4 of their papers we have counts for
4 papers
Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions
Folkmar Bornemann
We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical -dimensional Gaussian and Laguerre ensembles, now studying…
Algebraic Independence of an Airy Function, Its Derivative, and Antiderivative
Folkmar Bornemann
Using tools from the Siegel-Shidlovskii theory of transcendental numbers, we prove that a nontrivial solution of the Airy equation, its derivative, and an antiderivative are algebr…
Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities
Folkmar Bornemann
We continue our work [arXiv:2403.07628] on asymptotic expansions at the soft edge for the classical -dimensional Gaussian and Laguerre random matrix ensembles. By revisiting the…
Asymptotic Expansions of the Limit Laws of Gaussian and Laguerre (Wishart) Ensembles at the Soft Edge
Folkmar Bornemann
The large-matrix limit laws of the rescaled largest eigenvalue of the orthogonal, unitary, and symplectic -dimensional Gaussian ensembles -- and of the corresponding Laguerre en…